左删失数据的双惩罚贝叶斯Tobit分位回归方法  

Double Penalty Bayesian Tobit Quantile Regression Method for Left-censored Data

作　　者：舒婷 罗幼喜[1] 胡超竹 李翰芳 Shu Ting;Luo Youxi;Hu Chaozhu;Li Hanfang(School of Science,Hubei University of Technology,Wuhan 430068,China)

机构地区：[1]湖北工业大学、理学院,武汉430068

出　　处：《统计与决策》2023年第5期27-33,共7页Statistics & Decision

基　　金：国家社会科学基金资助项目(17BJY210);国家自然科学基金青年科学基金项目(11701161);湖北省教育厅人文社会科学研究重点项目(20D043);湖北工业大学博士科研启动项目(BSQD2020103)。

摘　　要：在含潜变量的纵向数据混合效应模型应用中,通常包含大量截尾数据,若直接采用一般贝叶斯Tobit分位回归模型,参数估计的马尔科夫链蒙特卡罗抽样算法将会极其复杂,造成计算效率低下且估计结果偏差较大。同时,在高维情形下,由于受大量未知随机效应的干扰,固定效应中关键变量的选择与系数估计变得更为困难。为了解决上述问题,文章提出了一种新的双Adaptive Lasso惩罚贝叶斯Tobit分位回归方法,主要研究响应变量左删失情形下高维纵向数据的变量选择与参数估计问题。通过将Adaptive Lasso惩罚同时引入固定效应与随机效应的先验分布中,构造了参数估计的Gibbs抽样算法。蒙特卡罗模拟结果表明,新方法较无惩罚法和Lasso惩罚法在重要变量选择及系数估计上均更占优势。In the application of longitudinal data mixed effect models with latent variables is usually included a large amount of censored data. If the general Bayesian Tobit quantile regression model is used directly, the Markov chain Monte Carlo(MCMC) sampling algorithm for parameter estimation will be extremely complex, resulting in low computational efficiency and large estimation deviation. At the same time, in the high dimensional case, as the model is disturbed by large number of unknown random effects, it is more difficult to select key variables and estimate coefficients in fixed effects. In order to solve the above problems, this paper proposes a new double Adaptive Lasso penalty Bayesian Tobit quantile regression method to study the variable selection and coefficient estimation of high dimensional longitudinal data model with left-censored response variables. By introducing Adaptive Lasso penalty into the prior distribution of fixed and random effects at the same time, a Gibbs sampling algorithm for parameter estimation is constructed. Monte Carlo simulation results show that the new method is more advantageous than the non-penalty method and Lasso penalty method in the selection of important variables and coefficient estimation.

关 键 词：删失混合效应模型 Adaptive Lasso惩罚 Tobit分位回归 Gibbs抽样算法 贝叶斯方法 

分 类 号：O212[理学—概率论与数理统计] F064.1[理学—数学]